Two regularization types as two different Nambu-Iona-Lasinio models
The Nambu-Iona-Lasinio models with 4-dimensional cutting and dimensional-analytical regularization types are compared. It is demonstrated that they describe two different models of light quark interaction. In the average-field approximation, the behavior of the scalar amplitude differs in the threshold region. Unlike the 4-dimensional cutting regularization in which the pole term corresponding to a sigma-meson can be separated near the threshold, the singularity of the scalar amplitude in the dimensional-analytical regularization is non-pole; moreover, it disappears completely for a certain value of the regularization parameter. One more significant difference between the two models is in the first-order expansion of the average field. The calculated meson contributions to the quark chiral condensate and dynamic quark mass demonstrate that despite their relative smallness, they can destabilize the Nambu-Iona-Lasinio model with 4-dimensional cutting regularization. On the contrary, the model with dimensional-analytical regularization is stabilized, which is manifested through a shift of regularization parameter values toward the stability region in which the contributions themselves decrease.
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- 9.R. G. Jafarov and V. E. Rochev, Centr. Eur. J. Phys., No. 2, 367 (2004) [hep-ph/0311339].Google Scholar
- 10.W. Ochs, Plenary talk at “Hadron 03” (Aschaffenburg, Germany) [hep-ph/031144].Google Scholar
- 12.E. Babayev, Phys. Rev., D62, 074020 (2000); G. Ripka, Nucl. Phys., A683, 463 (2001).Google Scholar
- 14.V. E. Rochev, Talk given at the 17th International Workshop on High-Energy Physics and Quantum Field Theory (QFTHEP’2003), Samara-Saratov (2003) [hep-ph/0312004].Google Scholar